Last July (2017), I shared the Combinatorics Mini Quilt. Then, at the end of September, I shared the Combinatorics: Paper Airplanes and Stars baby quilt. I have finally had a bit of time to pull some of my testing together and today I am looking forward to explaining more about what I mean by Combinatorics and share a fun block tutorial.

In the simplest sense, when I say “Combinatorics”, I mean combining two quilt blocks together to create a new quilt block. The easiest example I can give is using two squares (which can be viewed as a block on their own) and combining them together to create Half-Square Triangles. Today, to introduce the Combinatorics idea, I’m sharing how to combine two stripe blocks to create a fun offset, staggered triangle block.

Gather Your Materials

Combinatorics Introductory Tutorial – Gather Materials

• (4) 5″ x 9 1/2″ rectangles of Fabric A (green)*
• (4) 5″ x 9 1/2″ rectangles of Fabric B (white)*
• Fabric marking device of your choice
• Rotary Cutter
• Rotary Cutting Mat
• Rotary Cutting Rulers (I used my 6″ x 24″ and 12 1/2″ square frosted OLFA rulers)

*Note that these block sizes are based on efficient use of 10″ squares.

Sew Base Blocks

Combinatorics Introductory Tutorial – Sew Base Blocks

Sew together (1) Fabric A and (1) Fabric B 5″ x 9 1/2″ rectangle, right sides together, along the long edge with a 1/4″ seam allowance. Set your seam and press as desired (to the dark or open). Finished base blocks should measure 9 1/2″ square.

Combinatorics – Combine the Base Blocks

Combinatorics Introductory Tutorial – Combinatorics – Combine the Base Blocks

Using your fabric marking device of choice, mark a diagonal line from corner to corner on the wrong side of one base block. Note that Fabric A (green) is at the top and Fabric B (white) is at the bottom and the diagonal line should run from the upper right to the lower left. Place the marked base block right sides together with a second base block that has Fabric A (green) on the left and Fabric B (white) on the right. Sew 1/4″ away from the marked diagonal line on both sides (also shown in the photo for clarity) just like you would to create half-square triangles.

Combinatorics Introductory Tutorial – Combinatorics – Combine the Base Blocks

Cut along the marked line, press to set seams, and press seams open to reveal the Combinatorics Introductory block!

Combinatorics Introductory Tutorial – Combinatorics – Combine the Base Blocks

The final step is to trim the blocks to size: 9″ square. Place the 45 degree line of your ruler along the sewn line and adjust the ruler to get 4 1/2″ in the center of the two triangle points. Trim two sides, rotate your block, align the cut edges with your 9″ ruler lines and trim the final two sides.

Combinatorics – Combine the Base Blocks {Alternate Direction}

Combinatorics Introductory Tutorial – Combinatorics – Combine the Base Blocks Alternate Direction

To get the triangles in the Combinatorics Introductory Block to be a mirror image, the base blocks need to be sewn together in an alternate / second way. In the alternate block, mark a diagonal line on the wrong side of a base block with Fabric A (green) at the top and Fabric B (white) at the bottom running from the upper left to the lower right. Pair the marked base block with a second base block, right sides together. The second block should have Fabric A (green). on the right and Fabric B (white) on the left. Sew 1/4″ away from the marked diagonal line on both sides (also shown in the photo for clarity) just like you would to create half-square triangles. Cut along the marked line, press to set seams, and press seams open to reveal the alternate Combinatorics Introductory block.

Combinatorics Introductory Tutorial – Combinatorics – Combine the Base Blocks Alternate Direction

Trim the alternate block to 9″ square. Place the 45 degree line of your ruler along the sewn line and adjust the ruler to get 4 1/2″ in the center of the two triangle points. Trim two sides, rotate your block, align the cut edges with your 9″ ruler lines and trim the final two sides.

Finished Combinatorics Introductory Blocks

Combinatorics Introductory Tutorial Blocks

The top row of blocks above are made from the first two base blocks and the bottom row of blocks are made from the alternate direction instructions.

Combinatorics Introductory Tutorial Blocks

A quick rearrangement shows how the blocks can be combined to make the Combinatorics Mini Quilt layout!

I have many other ideas for how to create fun blocks from combinations of base blocks, and I look forward to sharing them with you soon. In the mean time, I am linking up with the Fall 2018 Tips and Tutorials Festival.